Increasing the Robustness of Point Operations in Co-Z Arithmetic against Side-Channel Attacks




Almohaimeed, Ziyad Mohammed

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Elliptic curve cryptography (ECC) has played a significant role on secure devices since it was introduced by Koblitz and Miller more than three decades ago. The great demand for ECC is created by its shorter key length while it provides an equivalent security level in comparison to previously introduced public-key cryptosystems (e.g.RSA). From an implementation point of view a shorter key length means a higher processing speed, smaller power consumption, and silicon area requirement. Scalar multiplication is the main operation in Elliptic Curve Diffie-Hellman (ECDH), which is a key-agreement protocol using ECC. As shown in the prior literature, this operation is both vulnerable to Power Analysis attack and requires a large amount of time. Therefore, a lot of research has focused on enhancing the performance and security of scalar multiplication. In this work, we describe three schemes to counter power analysis cryptographic attacks. The first scheme provides improved security at the expense of a very small cost of additional hardware overhead; its basic idea is to randomize independent field operations in order to have multiple power consumption traces for each point operation. In the second scheme, we introduce an atomic block that consists of addition, multiplication and addition [A-M-A]. This technique provides a very good scalar multiplication protection but with increased computation cost. The third scheme provides both security and speed by adopting the second tech- nique and enhancing the instruction-level parallelism at the atomic level. As a result, the last scheme also provides a reduction in computing time. With these schemes the users can optimize the trade-off between speed, cost, and security level according to their needs and resources.



elliptic curve cryptography, power analysis, Elliptic curve Diffie-Hellman, ECDH, ECC, atomic block, Countermeasure against Side-Channel Attacks, Side-Channel Attack Aware Implementation